Astronomy & Astrophysics manuscript no. Barbarians c ESO 2017 July 21, 2017

Shape and spin determination of Barbarian M. Devogèle1, 2, P. Tanga2, P. Bendjoya2, J.P. Rivet2, J. Surdej1, J. Hanuš2, 3, L. Abe2, P. Antonini4, R.A. Artola5, M. Audejean4, 7, R. Behrend4, 8, F. Berski9, J.G. Bosch4, M. Bronikowska6, A. Carbognani12, F. Char10, M.-J. Kim11, Y.-J. Choi11, C.A. Colazo5, J. Coloma4, D. Coward13, R. Durkee14, O. Erece15, 16, E. Forne4, P. Hickson17, R. Hirsch9, J. Horbowicz9, K. Kaminski´ 9, P. Kankiewicz18, M. Kaplan15, T. Kwiatkowski9, I. Konstanciak9, A. Kruszewki9,V. Kudak19, 20, F. Manzini4, 21, H.-K. Moon11, A. Marciniak9, M. Murawiecka22, J. Nadolny23, 24, W. Ogłoza25, J.L Ortiz26, D. Oszkiewicz9, H. Pallares4, N. Peixinho10, 27, R. Poncy4, F. Reyes28, J.A. de los Reyes29, T. Santana–Ros9, K. Sobkowiak9, S. Pastor29, F. Pilcher30, M.C. Quiñones5, P. Trela9, and D. Vernet2

(Aliations can be found after the references)

Received . . . ; accepted . . .

ABSTRACT

Context. The so-called Barbarian asteroids share peculiar, but common polarimetric properties, probably related to both their shape and composition. They are named after (234) Barbara, the first on which such properties were identified. As has been suggested, large scale topographic features could play a role in the polarimetric response, if the shapes of Barbarians are particularly irregular and present a variety of scattering/incidence angles. This idea is supported by the shape of (234) Barbara, that appears to be deeply excavated by wide concave areas revealed by and stellar occultations. Aims. With these motivations, we started an observation campaign to characterise the shape and rotation properties of Small Main- Belt Spectroscopic Survey (SMASS) type L and Ld asteroids. As many of them show long rotation periods, we activated a worldwide network of observers to obtain a dense temporal coverage. Methods. We used light-curve inversion technique in order to determine the sidereal rotation periods of 15 asteroids and the con- vergence to a stable shape and pole coordinates for 8 of them. By using available data from occultations, we are able to scale some shapes to an absolute size. We also study the rotation periods of our sample looking for confirmation of the suspected abundance of asteroids with long rotation periods. Results. Our results show that the shape models of our sample do not seem to have peculiar properties with respect to asteroids with similar size, while an excess of slow rotators is most probably confirmed. Conclusions. Key words. asteroids – asteroid shape – asteroid rotation

1. Introduction surfaces derivation technique (FSDT) which considers flat sur- faces on such models to obtain indications about the possible Shape modeling is of primary importance in the study of aster- presence of large concavities. oid properties. In the last decades, 1000 asteroids have had a shape model determined by using inversion⇠ techniques1; most of Cellino et al. (2006) reported the discovery of the anomalous them are represented by convex shape models. This is due to the polarimetric behaviour of (234) Barbara. Polarisation measure- fact that the most used technique when inverting the observed ments are commonly used to investigate asteroid surface proper- light-curves of an asteroid – the so-called light-curve inversion – ties and . Usually, the polarisation rate is defined as the is proven to mathematically converge to a unique solution only di↵erence of the photometric intensity in the directions paral- if the convex hypothesis is enforced (Kaasalainen and Torppa lel and perpendicular to the scattering plane (normalised to their I I ? k 2001; Kaasalainen et al. 2001). At the typical phase angles ob- sum): Pr = I +I . It is well known that the intensity of polarisa- served for Main Belt asteroids, the light-curve is almost insen- tion is related? tok the phase angle, that is, to the angle between sitive to the presence of concavities according to Durechˇ and the light-source direction and the observer, as seen from the ob- Kaasalainen (2003). Although the classical light-curve inver- ject. The morphology of the phase-polarisation curve has some sion process cannot model concavities, Kaasalainen et al. (2001) general properties that are mainly dependent on the of the point out that the convex shape model obtained by the inversion surface. A feature common to all asteroids is a “negative polari- is actually very close to the convex hull of the asteroid shape. sation branch” for small phase angles, corresponding to a higher Since the convex hull corresponds to the minimal envelope that polarisation parallel to the scattering plane. For most asteroids, contains the non-convex shape, the location of concavities cor- the transition to positive polarisation occurs at an “inversion an- responds to flat areas. Devogèle et al. (2015) developed the flat gle” of 20. In the case of (234) Barbara, the negative polarisa- tion branch⇠ is much stronger and exhibits an uncommonly large 1 See the Database of Asteroid Models from Inversion Techniques value for the inversion angle of approximately 30. Other Bar- (DAMIT) data base for an up-to-date list of asteroid shape models: barians were found later on (Gil-Hutton et al. 2008; Masiero and http://astro.troja.m↵.cuni.cz/projects/asteroids3D/ Cellino 2009; Cellino et al. 2014; Gil-Hutton et al. 2014; Bag-

Article number, page 1 of 23 A&A proofs: manuscript no. Barbarians nulo et al. 2015; Devogèle et al. 2017), and very recently, it was of some individual asteroids are presented as well as a general discovered that the family of Watsonia is composed of Barbar- discussion about the main results of the present work. The inci- ians (Cellino et al. 2014). dence of concavities and the distribution of the rotation periods Several hypotheses have been formulated in the past to ex- and pole orientations of L-type asteroids are presented. Finally plain this anomaly. Strong backscattering and single-particle Sect. 5 contains the conclusions of this work. scattering on high-albedo inclusions were invoked. Near- infrared (NIR) spectra exhibit an absorption feature that has been related to the presence of spinel absorption from flu↵y- 2. The observation campaigns type Calcium-Aluminium rich Inclusions (CAIs) (Sunshine et al. 2.1. Instruments and sites 2007, 2008). The meteorite analogue of these asteroids would be similar to CO3/CV3 meteorites, but with a surprisingly high CAI Our photometric campaigns involve 15 di↵erent telescopes and abundance ( 30%), never found in Earth samples. If this inter- sites distributed on a wide range in Earth longitudes in order pretation is confirmed,⇠ the Barbarians should have formed in an to optimise the time coverage of slowly rotating asteroids, with environment very rich in refractory materials, and would con- minimum gaps. This is the only strategy to complete light-curves tain the most ancient mineral assemblages of the Solar System. when the rotation periods are close to 1 , or longer, for This fact link, the explanation of the polarisation to the pres- ground-based observers. ence of high-albedo CAIs, is the main motivation for the study The participating observatories ( Center (MPC) of Barbarians, whose composition challenges our knowledge on code in parentheses) and instruments, ordered according to their meteorites and on the mechanisms of the formation of the early geographic longitudes (also Tab. 1), are: Solar System. – the 0.8m telescope of Observatori Astronòmic del Montsec The compositional link is confirmed by the evidence that all (OAdM), Spain (C65), Barbarians belong to the L and Ld classes of the Small Main- – the 1.04m “Omicron” telescope at the Centre Pédagogique Belt Asteroid Spectroscopic Survey (SMASS) taxonomy (Bus Planète et Univers (C2PU) facility, Calern observatory (Ob- and Binzel 2002), with a few exceptions of the K class. While servatoire de la Côte d’Azur), France (010), not all of them have a near-infrared spectrum, all Barbarians are – the 0.81m telescope from the Astronomical Observatory of found to be L-type in the DeMeo et al. (2009) NIR-inclusive the Autonomous Region of the Aosta Valley (OAVdA), Italy classification (Devogèle et al. 2017). (B04), However, the variety of polarimetric and spectroscopic prop- – the 0.4m telescope of the Borowiec Observatory, Poland erties among the known Barbarians, also suggests that composi- (187), tion cannot be the only reason for the anomalous scattering prop- – the 0.6m telescope from the Mt. Suhora Observatory, Cra- erties. In particular, Cellino et al. (2006) suggested the possible cow, Poland, presence of large concavities on the asteroid surfaces, resulting – the 0.35m telescope from Jan Kochanowski University in in a variety of (large) scattering and incidence angles. This could Kielce, Poland (B02), have a non-negligible influence on the detected polarisation, but – the 1m Zadko telescope near Perth, Australia (D20), such a possibility has remained without an observational verifi- – the 0.61m telescope of the Sobaeksan Optical Astronomy cation up to now. Observatory (SOAO), South Korea (345), Recent results concerning the prototype of the class, – the 0.7m telescope of Winer Observatory (RBT), Arizona, (234) Barbara, show the presence of large-scale concavities USA (648), spanning a significant fraction of the object size. In particu- – the 0.35m telescope from the Organ Mesa Observaory lar, interferometric measurements (Delbo et al. 2009) and well- (OMO), NM, USA (G50), sampled profiles of the asteroid obtained during two stellar oc- – the 0.6m telescope of the Southern Association for Re- cultations indicate the presence of large-scale concave features search in Astrophysics (SARA), La Serena Observatory, (Tanga et al. 2015). Testing the shape of other Barbarians for the Chile (807), presence of concavities is one of the main goals of the present – the 0.35m telescope from the UBC Southern Observatory, La study, summarising the results of several years of observation. Serena Observatory, Chile (807), To achieve this goal, we mainly exploit photometry to determine – the 1.54m telescope of the Estaciòn Astrofìsica de Bosque the shape, to be analysed by the FSDT. We compare our results Alegre (EABA), Argentina (821), the 1.5m telescope of the Instituto Astrofìsica de Andalucìa with the available occultation data (Dunham et al. 2016) in or- – (IAA) in Sierra Nevada, Spain (J86), der to check the reliability of the inverted shape model, scale – the 0.77m telescope from the Complejo Astronømico de La in size, and constrain the spin axis orientation. We also intro- Hita, Spain (I95). duce a method capable of indicating if the number of available light-curves is sucient to adequately constrain the shape model All observations were made in the standard V or R band as solution. well as sometimes without any filter. The CCD images were re- As we derive rotation periods in the process, we also test an- duced following standard procedures for flat-field correction and other evidence, rather weak up to now: the possibility that Bar- dark/bias subtraction. Aperture photometry was performed by barians contain an abnormally large fraction of “slow” rotators, the experienced observers operating the telescopes, and the aux- with respect to a population of similar size. This peculiarity – if iliary quantities needed to apply the photometric inversion (light- confirmed – could suggest a peculiar past history of the rotation time delay correction, asterocentric coordinates of the and properties of the Barbarians. the Earth) were computed for all the data. The article is organised as follows. In Sect. 2, we describe the The whole campaign is composed of 244 individual light- observation campaign and the obtained data. Sect. 3 presents the curves resulting from approximatively 1400 of observa- approach that was followed to derive the shape models. A new tion and 25000 individual photometric measurements of aster- method for analysing the shape model of asteroids is presented oids. All the new data presented in this work are listed in Table and tested on well-known asteroids. In Sect. 4, the characteristics A1 of Appendix A.

Article number, page 2 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Observat. D Longitude Latitude MPC Nlc Table 2 lists the class in the Tholen (Tholen 1984), SMASS [m] code (Bus and Binzel 2002; Mothé-Diniz and Nesvorný2008) and OAdM 0.8 00044013” 4201028” C65 16 Bus-Demeo (DeMeo et al. 2009; Bus 2009) taxonomies of the 15 C2PU 1.04 00656000” 4345000” 010 89 asteroids observed by our network. Each known Barbarian from OAVdA 0.81 00728042” 4547023” B04 16 is labelled as “Y” in the corresponding column. The Borowiec 0.4 01652048” 5224000” 187 41 number of the family parent member is given in the correspond- Suhora 0.60 02004001” 4934009” - 2 ing column. The bottom part of Table 2 gives the same informa- Kielce 0.35 02039024” 5052052” B02 2 tion for asteroids not observed by our network, but included in Zadko 1 11542049” 3121024” D20 9 this work to increase the sample. SOAO 0.61 12827027” 3656004” 345 4 RBT 0.7 24801015” 3142000” 648 21 OMO 0.35 25319048” 3217046” G50 11 3. Modelling method and validation of the results SARA 0.6 289 11 47” 30 10 10” 807 11 0 0 3.1. Shape modelling UBC 0.35 289 11 37” 30 10 07” 807 15 0 0 EABA 1.54 29527025” 3135046” 821 12 The sidereal rotation period was searched for by the light-curve IAA 1.5 35636051” 3703047” J86 5 inversion code described in Kaasalainen and Torppa (2001) and LA HITA 0.77 3564805000 393400700 I95 1 Kaasalainen et al. (2001) over a wide range. The final period is Table 1. List of the observatories participating in the observation cam- the one that best fits the observations. It is considered as unique paigns, with telescope aperture (D), position, and number of light- if the chi-square of all the other tested periods is > 10% higher. curves. A rather good longitude coverage was ensured. In order to obtain a more precise solution, sparse data are also included in the procedure, as described by Hanušet al. (2013). When the determination of a unique rotation period is possible, the pole solution(s) can be obtained. As is well known, paired In addition to these observations, we exploited light-curves solutions with opposite pole longitudes (i.e. di↵ering by 180 ) published in the literature. For the most ancient light-curves, the can fit the data equally well. If four or less pole solutions (usually APC (Asteroid Photometric Catalogue (Lagerkvist et al. 2001)) two sets of two mirror solutions) are found, the shape model is was used. The most recent ones are publicly available in the ˇ computed using the best fitting pole solution. DAMIT database (Durech et al. 2010). The accuracy of the sidereal rotation period is usually of As explained in the following section, we also used sparse the order of 0.1 to 0.01 times the temporal resolution interval photometry following the approach of Hanušet al. (2011, 2013). P2/(2T) (where P is the rotation period and T is the length of The selected data sets come from observations from the United the total observation time span). For the typical amount of op- ↵ States Naval Observatory (USNO)-Flagsta station (Interna- tical photometry we have for our targets the spin axis orienta- tional Astronomical Union (IAU) code 689), Catalina Sky Sur- tion accuracy for the light-curve inversion method is, in general, vey Observatory (CSS, IAU code 703 (Larson et al. 2003)), and 5/ cos for and 10 for (Hanušet al. 2011). Lowell survey (Bowell et al. 2014). ⇠ All possible shapes⇠ were compared with the results derived The already published data used in this work are listed in from stellar occultations whenever they were available. The pro- Table B1 of Appendix B. jected shape model on the sky plane is computed at the occulta- tion using the Durechˇ et al. (2011) approach. Its profile is 2.2. The target sample then adjusted, using a Monte-Carlo-Markov-Chain algorithm, to the extremes of the occultation chords. We coordinated the observation of 15 asteroids, selected on the With this procedure, the best absolute scale of the model is basis of the following criteria: found, thus allowing us to determine the size of the target. For – Known Barbarians, with a measured polarimetric anomaly; ease of interpretation, the absolute dimensions of the ellipsoid – SMASS L or Ld type asteroids, exhibiting the 2 µm spinel best fitting- the scaled shape model and the volume-equivalent absorption band; sphere Req are computed. – members of dynamical families containing known Barbar- In some cases, the result of stellar occultations also allows ↵ ians and/or L-type asteroids: Watsonia (Cellino et al. 2014), one to discriminate di erent spin axis solutions. the dispersed Henan (Nesvornýet al. 2015); Tirela (Mothé- Eventually, the FSDT is used to analyse all the derived con- Diniz and Nesvorný2008), renamed Klumpkea in Milani et vex shape models. As this procedure depends on the presence of al. (2014). flat surfaces, we must ensure that the shape models are reliable. In fact, portions of the asteroid surface not suciently sampled Fig. 1 shows the location (red dots) in semi-major axis and by photometry, can also produce flat surfaces. We thus estab- inclination of the asteroids studied in this work. In general, Bar- lished the approach explained in the following section, allowing barians are distributed all over the main belt. The concentration us to estimate the reliability of a shape derived by the light-curve in certain regions is a direct consequence of the identification of inversion. the Watsonia, Henan, and Tirela families. Future spectroscopic surveys including objects with a smaller diameter could better 3.2. Shape validation by the bootstrap method portray the global distribution. For each of the 15 asteroids that have been targeted in this Our goal is to evaluate the reliability of shape model details, and work, our observations have led to the determination of a new to check if a set of light-curves provides a good determination of rotation period, or increase the accuracy of the previously known the spin parameters. one. For eight of them, the light-curves dataset was suciently As mentioned above, the light-curve inversion process often large to determine the orientation of the spin axis and a reliable provides several sets of spin parameters (rotation period and spin convex shape model. axis orientation) that fit the optical data equally well. In other

Article number, page 3 of 23 A&A proofs: manuscript no. Barbarians

25

20 387 729

1372 15552 980 15 234 67255

458 402

10 172 1702 Inclination (i) [°] 824 236

5 2085 3844

1332 122

0 2 2.5 3 3.5 Semi-major axis (a) [AU]

Fig. 1. Inclination versus semi-major axis plot of main-belt asteroids. The asteroids studied in this work are plotted as red circular dots, while the thinner blue dots represent the asteroid population as a whole. cases, when only a few light-curves are available, the parameter inversion computation. If di↵erent sets of spin parameters set may converge with a single, but incorrect solution, often as- are found with equal probability, the whole procedure is ex- sociated with an incorrect rotation period. We see below that the ecuted for each of them. bootstrapping method detects such cases. Our approach consists in computing the shape model that – Once all the shape models are determined, we apply the best fits a subset of light-curves, randomly selected among all FSDT in order to find the best value of ⌘s for each shape those that are available for a given asteroid. By studying how the model. ⌘ fraction of flat surfaces s evolves with the number of selected – The last step consists in determining the mean value and the light-curves, we obtain a solid indication on the completeness of dispersion of ⌘s corresponding to each subset group charac- the data, that is, the need for new observations or not. terised by nl = 1, 2, 3, ..., Ndl light-curves. In more detail, we proceed as follows:

– First, a large number of light-curve samples is extracted from An excess of flat surfaces is often interpreted as the qual- the whole data set. Each of these subsets may contain a num- itative indication that the available photometry does not con- ber of light-curves nl ranging from nl = 1 to all those avail- strain the shape model adequately. The addition of supplemen- able (nl = Ndl). Sets of sparse data are also included in the tary light-curves is then a necessary condition to improve the process and equal for all samples. In fact, the availability of shape. In our procedure, we make the hypothesis that, as the a sparse data set is a necessary condition to apply the boot- number of light-curves increases, the ⌘s parameter decreases. In strapping technique. Since shape models can sometimes be the process, the model converges to the convex hull of the real derived using sparse data only, they allow the inversion pro- shape. Ideally, the only flat surfaces remaining should then cor- cess to converge to a solution even for low values of nl. respond to concave (or really flat) topological features. Such a – The second step consists in deriving the shape model cor- convergence should ideally show up as a monotonic decrease of responding to all the light-curve samples generated in the ⌘s towards an asymptotic value for a large nl. Here, we apply our previous step. The spin axis parameters found by using all procedure and show that our quantitative analysis is consistent the light-curves are exploited as initial conditions for each with this assumption.

Article number, page 4 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Asteroid Tholen SMASS DM Barbarian Family

(122) Gerda ST L (172) Baucis SL Y (234) Barbara S Ld L Y (236) Honoria SL L Y (387) Aquitania SL L Y (402) Chloe SK L Y (458) Hercynia SL Y (729) Watsonia STGD L L Y 729 (824) Anastasia SL L (980) Anacostia SU L L Y (1332) Marconia Ld L (1372) Haremari L 729 (1702) Kalahari DL (2085) Henan LL 2085 (3844) Lujiaxi LL 2085 (15552) Sandashounkan 1400 (234) Barbara S Ld L Y (599) Luisa SK L Y (606) Brangane TSD K L 606 (642) Clara SL (673) Edda SS L (679) Pax IKL Y (1284) Latvia TL (2448) Sholokhov LL Table 2. List of the targets observed by our network (upper part). Some targets that were not observed by us but discussed in this work were added in the lower part. The first column corresponds to the number and name of the considered asteroid. The columns Tholen (Tholen 1984), SMASS (Bus and Binzel 2002; Mothé-Diniz and Nesvorný2008) and Bus-Demeo (DM) (DeMeo et al. 2009; Bus 2009) stand for the taxonomic class in these three types of taxonomy. The Barbarian column indicates whether or not the asteroid is considered as a Barbarian (Cellino et al. 2006; Gil-Hutton et al. 2008; Masiero and Cellino 2009; Bagnulo et al. 2015). Finally, the Family column indicates the number of the parent member of the family in which the asteroid is classified (606 for the Brangane, 729 for the Watsonia, 1400 for the Tirela/Klumpkea and 2085 for the Henan family).

We stress here that the number of possible subsets that can 0.7 be extracted is potentially large, as it is given by the binomial 433 Eros N coecient k . 0.6 f(x) = a exp( - b x) + c a = 0.49573 b = 0.017975 If the number⇣ ⌘ of light-curves is below 14, all subsets are ex- c = 0.13405 ploited. If there are additional light-curves, the number of pos- 0.5 R = 0.99113 (lin) sible combinations increases, but we do not generate more than 10, 000 random subsets to limit the computation time. Our re- 0.4 sults show that this is not a limitation when the light-curve sam- ple is very rich. 0.3 Mean fraction of flat surfaces 0.2 3.2.1. Test on (433) Eros 0.1 0 20 40 60 80 100 120 140 The bootstrap method was first tested on (433) Eros for which Number of the shape is well known thanks to the images taken by the NEAR Bootstrap curves for the asteroid (433) Eros mission (Gaskell 2008). A large number of dense photometric Fig. 2. light-curves (N = 134) is also available for this asteroid which allows us to derive an accurate shape model using light-curve that would be detected if a very large number of light-curves was inversion. used. In the case of (433) Eros we find ⌘a = 0.134. The data set of (433) Eros contains 134 dense light-curves For a comparison to the “real” shape, we can take advantage and 2 sets of sparse data. Fig. 2 shows the average of the flat of the detailed shape model of (433) Eros obtained by the analy- surface fraction (⌘s) as a function of the number of dense light- sis of the NEAR space probe images, obtained during the close curves (Ndl) used for the shape modelling. encounter. For our goal, a low-resolution version (Gaskell 2008) As expected (Fig. 2), the ⌘s versus Ndl curve (hereafter called is sucient, and was used to check the result described above. the bootstrap curve) is monotonically decreasing. It is straight- By taking the convex-hull (i.e. the smallest convex volume forward to verify that an exponential function y = a exp ( bx)+c that encloses a non-convex shape), we obtain the shape model is well suited to fit the bootstrap curve. In this expression the c that, in an ideal case, the light-curve inversion should provide. parameter corresponds to the asymptotic value ⌘a, that is, the ⌘s In that specific case, the FSDT yields ⌘a = 0.12. This value is

Article number, page 5 of 23 A&A proofs: manuscript no. Barbarians within 6% of the value obtained by the bootstrapping method. 4. Results and interpretation This is a first indication that our approach provides a good ap- proximation and can be used to evaluate the “completeness” of In Fig. 4, one example of a composite light-curve for two as- a light-curve set. teroids observed by our network is shown. For each target, the synodic period (Psyn) associated to the composite light-curve is We may compare our result to the value corresponding to provided. Additional light-curves are displayed in Appendix C. the complete set of Ndl available light-curves. In this case, For the cases where too few light-curves have been obtained by ⌘s = 0.18, a much larger discrepancy (20%) with respect to the our survey to derive a reliable synodic period, the sidereal pe- correct value. This result means that the convex shape model riod (Psid) determined based on multi-opposition observations of (433) Eros (derived by photometry only) could probably be and obtained by the light-curve inversion method is used as an somewhat improved by adding new dense light-curves. initial guess. In the case of (824) Anastasia, no error bars are In the following sections, we apply this analysis to other ob- provided since our observations were obtained during only one jects for the evaluation of their shape as derived from the photo- (very long) revolution. In Fig. 5 is displayed two examples of metric inversion. shape model derived in this work. Additional shape models are displayed in Appendix D. The bootstrap curves (see Sec. 3.2.1) are also shown for the di↵erent solutions of the pole orientation 3.2.2. Sensitivity of the bootstrap method to the spin axis (except for (387) Aquitania for which no sparse data were used). coordinates Table 3 summarises the information about these asteroids, whose physical properties have been improved by our observations. Ta- The behaviour of the bootstrap curve (exponentially decreasing) ble 4 is the same as Table 3, except that it lists asteroids that we is related to the choice of the correct spin axis parameters. did not directly observe ourselves, but that are relevant to our This property is illustrated on the asteroid (2) Pallas. Even discussion. though Pallas has not been visited by a space probe, its spin axis orientation and shape are well known thanks to stellar occulta- 4.1. Individual asteroids tions and adaptive optics observations (Carry et al. 2010). In the following we compare our results for each asteroid to The other di↵erence with the case of (433) Eros is that there some data available in the literature; asteroid occultation results are less observed dense light-curves. As a matter of fact, the (Dunham et al. 2016) in particular. light-curve inversion provides two ambiguous solutions for the In Figs. 6 to 9, the occultations data are represented in the spin axis coordinates, at (37.9 , 15.1 ) and (199.6 , 39.4 ). Both so-called fundamental plane (i.e. the plane passing through the poles yield the same RMS residuals for the fit to the light-curves. centre of the Earth and perpendicular to the observer-occulted A priori, there is no way to know which solution is the star vector) (Durechˇ et al. 2011). In that plane, the disappear- best, without additional constraint such as disk-resolved obser- ance and reappearance of the occulted star are represented re- vations, since both solutions reproduce equally well the observed spectively by blue and red squares and the occultation chords photometry. However, there is a clear di↵erence between the represented by coloured continuous segments. Error bars on the two when analysing the bootstrap curve (Fig. 3). The first solu- disappearance and reappearance absolute timing are represented tion follows the well-defined exponential convergence providing by discontinuous red lines. Negative observations (no occulta- ⌘a = 0.045, which seems to be consistent with the shape model tion observed) are represented by a continuous coloured line. as it is known so far. For the second spin axis orientation so- Discontinuous segments represent observations for which no ab- lution, we see that the bootstrap curve does not seem to follow solute timing is available. For each asteroid, the corresponding the exponential trend. The corresponding ⌘ 0.15 is in contra- a ⇠ volume-equivalent radius is computed (corresponding to the ra- diction with the fact that the shape of (2) Pallas does not show dius of a sphere having the same volume as the asteroid shape any sign of large concave topological features. The rejection of model). The dimensions of the ellipsoid best fitting the shape the second pole solution is consistent with the result of stellar model are also given. The uncertainties on the absolute dimen- occultations and adaptive optics (Carry et al. 2010). sions of the shape models adjusted to stellar occultations are de- rived by varying various parameters according to their own un- certainties. First, the di↵erent shape models obtained during the 3.2.3. Distribution of flat surfaces across the available bootstrap method are used. The spin axis parameters are ran- shape-model population. domly chosen according to a normal distribution around their nominal values with standard deviation equal to the error bars The bootstrap method gives us information on the possible pres- given in Table 3. Finally the extremes of each occultation chord ence of concave topological features. Here, a large number of as- are randomly shifted according to their timing uncertainties. The teroid shape models are analysed. These shape models are used observed dispersion in the result of the scaling of the shape as a reference population with which the derived shape models model on the occultations chords is then taken as the formal un- of Barbarians can be compared. certainty on those parameters. This reference was constructed using the shape models avail- The list of all the observers of asteroid occultations which able on the DAMIT database (Durechˇ et al. 2010). More than 200 are used in this work can be found in Appendix D (Dunham et asteroid shape models were analysed. For many of them, the re- al. 2016). In the following we discuss some individual cases. sult of the bootstrap method clearly shows that more data would (172) Baucis - There are two reported occultations. The first be needed to obtain a stable shape. In a minority of cases, we find event is a single-chord, while the other (18 December 2015) a behaviour suggesting incorrect pole coordinates. We selected a has two positive chords and two negative ones, and was used to sample of 130 shape models, for which the bootstrap curve had scale the shape model (Fig. 6). According to the fit of the shape the expected, regular behaviour towards a convergence, and for model to the occultation chords, both pole solutions seemed them we computed ⌘a. equally likely. The two solutions give similar absolute dimen-

Article number, page 6 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Spin solution (37.9°, -15.1°) Spin solution (199.6°, 39.4°) 0.35 0.35 Result of the bootstrap method Result of the bootstrap method Fit of a exp(-bx)+c Fit of a exp(-bx)+c 0.3 0.3

0.25 0.25

0.2 0.2

0.15 0.15

Fraction of flat surfaces 0.1 Fraction of flat surfaces 0.1

0 20 40 60 0 20 40 60 Number of lightcurves Number of lightcurves

Fig. 3. Bootstrap curves for the asteroid (2) Pallas. The panels illustrate the curve obtained for di↵erent coordinates of the spin axis.

2 0 Borowiec 131101 C2PU 040417 Borowiec 131202 C2PU 130417 2.05 Organ Mesa 140103 C2PU 130418 Organ Mesa 140110 0.05 C2PU 130424 Organ Mesa 140113 C2PU 130503 2.1 Organ Mesa 140127 C2PU 130506 Organ Mesa 140129 C2PU 130511 Borowiec 140205 0.1 C2PU 130512 C2PU 140207 C2PU 130513 2.15 Organ Mesa 140215 C2PU 130517 Organ Mesa 140219 0.15 C2PU 130519 C2PU 140217 C2PU 130520 2.2 Borowiec 140205 C2PU 130521 Kielce 140309 C2PU 130604 Borowiec 140313 0.2 C2PU 130605 Relative 2.25 Kielce 140320 Relative magnitude C2PU 130606

0.25 2.3

2.35 0.3 0 0.5 1 1.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Rotational phase Rotational phase (236) Honoria, P = 12.3373 0.0002 h (729) Watsonia, P = 25.19 0.03 h syn ± syn ± Fig. 4. Composite light-curves of two asteroids in our sample. Each light-curve is folded with respect to the synodic period of the object, indicated below the plot. sions of (41.1 2, 36.3 1.8, 31.8 1.6) and (40.8 2.4, 36.1 (387) Aquitania - For this asteroid, the result of the light- 1.7, 33.5 1.6)± km, respectively.± ± The corresponding± volume-± curve inversion process gives di↵erent solutions for the rotation ± equivalent radii are Req = 36.2 1.8 km and Req = 36.7 1.8 km, period when sparse data are included. However, the noise on the to be compared to the NEOWISE± (Mainzer et al. 2016),± sparse data is higher than the amplitude of the light-curves them- (Usui et al. 2012) and IRAS (Tedesco 1989) radii: 35.3 0.4, selves. For this reason we decided to discard them. As a conse- 33.5 0.4 and 31.2 0.6 km, respectively. Even though the± oc- quence, we did not apply the bootstrap method to this asteroid. ± ± cultation observations cannot provide information about the best There is one well sampled occultation of (387) Aquitania spin axis solution, the bootstrap curve indicates a clear prefer- providing four positive and four negative chords. The adjust- ence for the one with retrograde rotation. ment of the unique solution of the shape model on the occul- tation chords shows a good agreement. The scaling leads to an (236) Honoria - There are eight observed occultations. How- equivalent radius Req = 50.4 2.5 km. The absolute dimensions are (54.2 2.7, 50.6 2.5, 46.±6 2.3) km. This is consistent with ever, over these eight events, only two have two positive chords ± ± ± (in 2008 with two positive chords and 2012 with three pos- the WISE (Masiero et al. 2011), AKARI, and IRAS radii, which are respectively 48.7 1.7, 52.5 0.7, and 50.3 1.5 km. The fit itive chords). These were used to constrain the pole orienta- ± ± ± tion and scale the shape model. The result shows that the first of the shape model on the occultation chords is shown in Fig. 8. pole solution (1 and 1 from Table 3) is the most plausible. Hanušet al. (2017) found a relatively similar model, spin By simultaneously fitting the two occultations, the obtained di- axis solution (Psid = 24.14012 hours, = 123 5, and = ± mensions are (48.8 1.4, 48.3 1.3, 33.7 1.0) km, and the 46 5), and size (48.5 2 km) using an independent approach. ± ± ± ± ± volume-equivalent radius Req = 43.0 2.1 km. In the case of (402) Chloe - There are six reported occultations, but only the second pole solution, the dimensions± of the semi-axes are two can be used to adjust the shape models on the occultation (52.3 2.7, 52.1 2.6, 37.1 1.9) km and the equivalent radius chords. These two occultations occurred on the 15 and 23 De- ± ± ± is Req = 45.6 2.3 km. These solutions are compatible with the cember 2004. The result clearly shows that the first pole so- NEOWISE, AKARI,± and IRAS measurements which are respec- lution is the best one. The other one would require a defor- tively 38.9 0.6, 40.6 0.5 and 43.1 1.8 km. The fit of the shape mation of the shape that would not be compatible with the model for the± two pole± solutions is shown± in Fig. 7. constraints imposed by the negative chords. The derived di-

Article number, page 7 of 23 A&A proofs: manuscript no. Barbarians

(172) Baucis, pole solution (14, 57).

(236) Honoria, pole solution (196, 54). Fig. 5. Example of two asteroid shape models derived in this work. For both shape model, the reference system in which the shape is described by the inversion procedure, is also displayed. The z axis corresponds to the rotation axis. The y axis is oriented to correspond to the longest direction of the shape model on the plane perpendicular to z. Each shape is projected along three di↵erent viewing geometries to provide an overall view. The first one (left-most part of the figures) corresponds to a viewing geometry of 0 and 0 for the longitude and latitude respectively (the x axis is facing the observer). The second orientation corresponds to (120, 30) and the third one to (240, 30). The inset plot shows the result of the Bootstrap method. The x axis corresponds to the number of light-curves used and the y axis is ⌘a.

60 (172) Baucis : 2015/12/18 λ = 170.6° 50 (172) Baucis : 2015/12/18 λ = 14.1° β = -63° β = -57.2° 40 P = 27.4097 h P = 27.4096 h sid sid

20

0 0 [km] [km] ξ ξ -20

-40 -50 -60 -50 0 50 -60 -40 -20 0 20 40 60 η [km] η [km]

Fig. 6. Fit of the derived shape models for (172) Baucis on the observed occultation chords from the 18 December 2015 event. The left panel represents the shape model corresponding to the first pole solution (1, 1). The right panel represents the shape model obtained using the second pole solution. mensions of (402) Chloe, for the first spin axis solution, are ond one. The fit of the shape model on the occultation chords is (38.3 1.9, 33.7 1.7, 24.7 1.2) km and the equivalent radius is shown in Fig. 9. R =±31.3 1.6 km.± The second± spin solution leads to the dimen- eq ± sions (46.9 2.4, 41.3 2.1, 29.0 1.5) km and Req = 38.3 1.9 (824) Anastasia - The light-curve inversion technique pro- km. The NEOWISE± radius± is 27.±7 0.8 km while the AKARI± vided three possible pole solutions. However, two of them and IRAS radii are 30.2 1.5 and± 27.1 1.4 km, respectively, present a rotation axis which strongly deviates from the prin- which agree with the first± pole solution,± but not with the sec- cipal axis of inertia. This is probably related to the extreme elon- gation of the shape model. The light-curve inversion technique is

Article number, page 8 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Aster. b/ac/b Psid 1 1 2 2 Ndl Nopp N689 N703 NLO ⌘a D [hours] [deg] [deg] [deg] [deg] [km] 122 0.85 0.96 10.6872 1 30 5 20 10 209 5 22 10 24 6 181 108 0 (70.7 0.9) 172 0.93 0.90 27.4097 ± 4 171± 11 64± 10 14 ±9 57± 10 61 6 159 75 0.17 77.4 ±3.9 236 0.88 0.86 12.3375 ± 1 196 ± 9 54 ±10 36 ± 7 44 ±10 57 5 187 120 0.16 86.0 ± 4.3 387 0.93 0.88 24.14 2± 142 ± 8 51 ± 10 ± ± 26 6 100.7± 5.3 402 0.88 0.70 10.6684± 1 306 ± 10 61± 10 162 7 41 10 15 4 169 65 0 64.6 ±3.2 ± ± ± ± ± ± 458 0.86 0.80 21.81 5 274 6 33 10 86 5 14 10 14 3 197 103 0.38 (36.7 0.4) ± ± ± ± ± ± 729 0.88 0.86 25.195 1 88 26 79 10 60 3 182 104 0.14 (50.0 0.4) 824 252.0 ±7 ± ± 25 2 133 149 (32.5 ± 0.3) ± ± 980 0.93 0.83 20.114 4 24.2 6 35 10 203 5 5 10 48 6 167 68 0.28 (74.7 0.6) 1332 32.120 ± 1 ± ± ± ± 16 2 408 (46.8 ± 0.1) ± ± 1372 15.23 4 18 2 84 60 (26.5 0.3 ) ± ± 1702 21.15 2 21 2 90 155 (34.6 0.1) ± ± 2085 111 1 12 1 27 93 (13.35 0.04) 3844 13.33± 2 10 1 87 (15.5 ±0.7) ± ± 15552 33.63 7 19 2 58 (6.2 0.2 ) ± ± Table 3. Summary of the results pertaining to our survey. The b/a and c/b columns represent the relative axis dimensions of the ellipsoid best fitting the shape model. The Psid column indicates the sidereal rotation period of the asteroid in hours. The uncertainties are given with respect to the last digit. Columns n and n, with n = 1 and 2, represent the two or the unique pole solution(s). The Nx columns represent respectively the number of dense light-curves, the number of oppositions and the number of sparse points from the USNO (MPC code 689), Catalina (MPC code 703) and Lowell surveys. ⌘a represents the fraction of flat surfaces present on the shape model as inferred by the bootstrap method. Finally, the D column represents the equivalent diameter of the sphere having the same volume as the asteroid shape model. When we were not able to scale the shape model of the asteroid, the NEOWISE diameter (Mainzer et al. 2016) (or WISE diameter (Masiero et al. 2011) when NEOWISE data are unavailable) is given in parentheses.

Asteroid b/ac/b Psid 1 1 2 2 ⌘a D Ref. [hours] [deg] [deg] [deg] [deg] [km] 234 0.90 0.88 26.474 144 38 0.33 43.7 [1] 599 9.3240 71 [2] 606 0.82 0.92 12.2907 183 20 354 26 35.5 [3] 642 8.19 38.2 [4] 673 22.340 41.6 [5] 679 0.72 0.92 8.45602 220 32 42 5 0.38 51.4 [6] 1284 9.55 46 [7] 2448 10.061 43 [8] Table 4. Same as Table 3, but for asteroids which were not observed during this campaign. The bootstrap method was not applied to (606) because the number of dense light-curves was not sucient. References : [1] Tanga et al. (2015), [2] Debehogne et al. (1977), [3] Hanušet al. (2011), [4] LeCrone et al. (2005), [5] Marciniak et al. (2016), [6] Marciniak et al. (2011), [7] Carreño-Carcerán et al. (2016), [8] Strabla et al. (2013)

known to have diculty in constraining the relative length along Fig. 10 presents the result of the FSDT for the shape mod- the axis of rotation, in particular. In the case of highly elongated els presented in this work (blue diamonds, see Tables 3 and 4). bodies, the principal axis of inertia is poorly constrained. These results can be compared to the average value of ⌘a com- Two occultations were reported for this asteroid. The mod- puted by bins of 15 asteroids (red squares) using the asteroid els cannot fit the two occultations simultaneously using a single population described in Sec. 3.2.3 (black dots). scale factor. We decided therefore not to present the shape model and spin solutions in this paper as new observations are required to better constrain the pole solution. Because of the very large rotation period of this asteroid, the presence of a possible tum- bling state should also be tested. From this distribution, a correlation between diameter and (2085) Henan - This asteroid possesses a relatively large ro- fraction of flat surfaces seems to be apparent. Such correlation tation period. Based on our photometric observation, two syn- is expected since small asteroids are more likely to possess ir- odic periods can be considered (110 1 hours and 94.3 1 hours). regular shapes than larger ones. However, the quality of aster- However, the light-curve inversion± technique seems± to support oid light-curves is directly correlated to the asteroids diameter. < ↵ the first one based on our observations and sparse data. For small asteroids ( 50 km), this e ect might also increase the mean value of ⌘a. Fig. 10 does not show clear di↵erences between Barbarians and other asteroids, as Barbarians seem to 4.2. Presence of concavities populate the same interval of values. As expected, some aster- oids like Barbara show a large amount of flat surfaces, but this We have applied the flat detection method (FSDT) described in is not a general rule for Barbarians. Of course the statistics are Devogèle et al. (2015) to all the shape models presented in this still not so high, but our initial hypothesis that large concave paper, thus (Sec. 3.2) providing a quantitative estimate for the topological features could be more abundant on objects having a presence of concavities and for the departure of an asteroid shape peculiar polarisation does not appear to be valid in view of this from a smooth surface with only gentle changes of curvature. first attempt of verification.

Article number, page 9 of 23 A&A proofs: manuscript no. Barbarians

60 (236) Honoria : 2008/10/11 λ = 196° (236) Honoria : 2012/9/7 λ = 196° β = 54.2° 60 β = 54.2° P = 12.3376 h 40 P = 12.3376 h sid sid 40 20 20

0 0 [km] [km] ξ ξ -20 -20

-40 -40

-60 -60 -50 0 50 -50 0 50 η [km] η [km]

60 (236) Honoria : 2008/10/11 λ = 36.2° (236) Honoria : 2012/9/7 λ = 36.2° β = 44.5° 60 β = 44.5° P = 12.3376 h P = 12.3376 h 40 sid sid 40 20 20 0

[km] [km] 0 ξ ξ -20 -20

-40 -40 -60 -60 -50 0 50 -50 0 50 100 η [km] η [km]

Fig. 7. Fit of the derived shape models for (236) Honoria on the observed occultation chords from the 11 October 2011 and the 7 September 2012 events. The left panel represents the 2008 event with the top and bottom panels corresponding to the first and second pole solutions, respectively. The right panel is the same as the left one, but for the 2012 event.

only asteroids with a diameter above 40 km, we are relatively

80 (387) Aquitania : 2013/7/26 λ = 142.4° sure that our sample of L-type asteroids is both almost com- β = 50.8° plete, and not a↵ected by the Yarkovsky-O’Keefe-Radzievskii- 60 P = 24.1402 h sid Paddack e↵ect (Bottke et al. 2006). However, as only 13 aster- 40 oids remain in the sample, we also consider a second cut at 30 20 km, increasing it to 18. As shown below, our findings do not 0 change as a function of this choice.

[km] We proceed by comparing the rotation period of the Barbar- ξ -20 ians with that of a population of asteroids that possess a similar -40 size distribution. Since the distribution of rotation periods is de- -60 pendent on the size of the asteroids, we select a sample of as- teroids with the same sizes, using the following procedure. For -80 each Barbarian, one asteroid is picked out randomly in a popula- -100 -50 0 50 100 tion for which the rotation period is known, and having a similar η [km] radiometric diameter within a 5 km range. This way we con- struct a population of asteroids± with the same size distribution Fig. 8. Fit of the derived shape model for (387) Aquitania on the ob- as the Barbarians. We now have two distinct populations that we served occultation chords from the 26 July 2013 event. can compare. By repeating this process several times, we build a large number of populations of ‘regular’ asteroids. We can then check the probability that the distribution of rotation periods of 4.3. Are Barbarian asteroids slow rotators ? such a reconstructed population matches the one of the Barbar- In this Section, we compare the rotation periods of Barbarians ians. and Barbarian candidates with those of non-Barbarian type. At Considering the sample of asteroids with a diameter larger first sight the rotation period of confirmed Barbarian asteroids than 40 km, the sample is too small to derive reliable statistics. seems to indicate a tendency to have long rotation periods, as the However, we notice that the median of the rotation period of number of objects exceeding 12h is rather large. For our analysis the Barbarians is 20.1 hours while the median of the population we use the sample of objects as in Tables 3 and 4. By considering regular asteroid is only 12.0 hours.

Article number, page 10 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

40 (402) Chloe : 2004/12/23 λ = 306.3° 40 (402) Chloe : 2004/12/15 λ = 306.3° β = -61.1° β = -61.1° P = 10.6684 h P = 10.6684 h 30 sid 30 sid

20 20 10 10

[km] [km] 0 ξ 0 ξ -10 -10 -20 -20 -30

-40 -20 0 20 40 -50 0 50 η [km] η [km]

60 (402) Chloe : 2004/12/15 λ = 163.5° 60 (402) Chloe : 2004/12/23 λ = 163.5° β = -43.8° β = -43.8° P = 10.6684 h P = 10.6684 h 40 sid 40 sid

20 20

[km] 0 [km] 0 ξ ξ

-20 -20

-40 -40

-50 0 50 -50 0 50 η [km] η [km]

Fig. 9. Fit of the derived shape models for (402) Chloe on the observed occultation chords from 15 and 23 December 2014 events. The leftmost part of the Figure represents the 15 event with the upper and lower parts corresponding to the first and second pole solutions, respectively. The rightmost part of the Figure is the same as the leftmost part, but for the 23 December event.

0.7 Individual asteroids Mean of individual asteroids 0.6 Barbarians 0.5

0.4

0.3

0.2

Fraction of flat surfaces 0.1

0 0 50 100 150 200 250 540 Diameter [Km]

Fig. 10. Values of ⌘a as a function of the asteroids diameters. The black dots correspond to individual asteroids. The red squares correspond to the mean values of ⌘a and diameter for bins of 15 asteroids. The blue diamonds correspond to Barbarian asteroids.

In order to improve the statistic, we can also take into ac- Fig. 11. Normalised histograms of the Barbarian compared to the his- count asteroids with a diameter between 30 and 40 km. The togram asteroids having a diameter between 110 and 30 km. median of the Barbarian asteroids is now 20.6 hours while the regular asteroids population has a median of 11.4 hours. Fig. 11 represents the histograms of the rotation periods of oids shows a clear excess of long rotation periods and a lack of Barbarian asteroids (with diameter > 30 km) compared to the fast-spinning asteroids. population of regular asteroids constructed as described at the We adopt the two-samples Kolmogorov-Smirnov (KS) test beginning of this section. The histogram of the Barbarian aster- to compare the distributions of Barbarians and regular asteroids.

Article number, page 11 of 23 A&A proofs: manuscript no. Barbarians

This is a hypothesis test used to determine whether two pop- SARA observations were obtained under the Chilean Tele- ulations follow the same distribution. The two-sample KS test scope Allocation Committee program CNTAC 2015B-4. returns the so-called asymptotic p-value. This value is an indi- PH acknowledges financial support from the Natural Sci- cation of the probability that two samples come from the same ences and Engineering Research Council of Canada, and thanks population. the sta↵ of Cerro Tololo Inter-American Observatory for techni- In our case, we found p = 0.6%, clearly hinting at two dis- cal support. tinct populations of rotation period. The work of AM was supported by grant no. In conclusion our results show that there is clear evidence 2014/13/D/ST9/01818 from the National Science Centre, that the rotations of Barbarian asteroids are distinct from those Poland. of the whole population of asteroids. The abnormal dispersion of The research of VK is supported by the APVV-15-0458 grant the rotation periods observed for the Barbarian asteroids is more and the VVGS-2016-72608 internal grant of the Faculty of Sci- probably the result of a true di↵erence than a statistical bias. ence, P.J. Safarik University in Kosice. MK and OE acknowledge TUBITAK National Observatory for a partial support in using T100 telescope with project number 5. Conclusions 14BT100-648. We have presented new observations here for 15 Barbarian or candidate Barbarian asteroids. For some of these asteroids, the References observations were secured by us during several oppositions. Bagnulo, S., Cellino, A., Sterzik, M.F., 2015, MNRAS Lett., 446, L11 These observations allow us to improve the value of the rotation Barucci M., Fulchignoni M., Burchi R. and D’Ambrosio V., 1985, Icarus, 61, period. For eight of them, we were able to determine or improve 152 the pole orientation and compute a shape model. Binzel R., 1987, Icarus, 72, 135 The shape models were analysed using a new approach based Bottke W.F., Vokrouhlick D., Rubincam D.P., Nesvorn D., 2006, Annual Review of Earth and Planetary Sciences, 34, 157 on the technique introduced by Devogèle et al. (2015). We show Bowell, E., Oszkiewicz, D. A., Wasserman, L. H., Muinonen, K., Penttilä, A., that this technique is capable of providing an indication about Trilling, D. E., 2014, Meteoritics & Planetary Science, 49, 95 the completeness of a light-curve data set indicating whether or Buchheim R., Roy R., Behrend R., 2007, The Minor Planet Bulletin, 34, 13 not further observations are required to better define a shape so- Bus S., Binzel R., 2002, Icarus, 158, 146 Bus, S. J., Ed., IRTF Near-IR Spectroscopy of Asteroids V1.0. EAR-A-I0046-4- lution of the photometric inversion method. The extrapolation of IRTFSPEC-V1.0. NASA Planetary Data System, 2009. the trend towards a large number of light-curves gives a more Carreõ-Carcerán, A. et al., 2016, MPBu, 43, 92 precise determination of ⌘s. This new method was applied to Carry B. et al., 2010, Icarus, 205, 460 a large variety of shape models in the DAMIT database. This Cellino A., Belskaya I. N., Bendjoya Ph., di Martino M., Gil-Hutton R., allowed us to construct a reference to which the shape models Muinonen K. and Tedesco E. F., 2006,Icarus, 180, 565 Cellino A., Bagnulo S., Tanga P., Novakivoc B., Delbo M., 2014, MNRAS, 439, determined in this work were compared. Our results show that 75 there is no evidence that our targets have more concavities or are Debehogne, H., Surdej, A., Surdej, J., 1977, A&A Suppl. Ser., 30, 375 more irregular than a typical asteroid. This tends to infirm the DeMeo F., Binzel R., Slivan S and Bus S, 2009, Icarus, 160, 180 hypothesis that large-scale concavities may be the cause of the Denchev P., Shkodrovb V. and Ivanovab V., 2000, Planetary and Space Science, 48, 983 unusual polarimetric response of the Barbarians. Delbo M., Ligori S., Matter A., Cellino A., Berthier J.,2009, The A.J., 694, 1228 The improvement and new determination of rotation peri- Devogèle M., Rivet J. P., Tanga P., Bendjoya Ph., Surdej J., Bartczak P., Hanus ods has increased the number of asteroids for which a reliable J., 2015, MNRAS, 453, 2232 rotation period is known. This allows us to have an improved Devogèle M. et al., 2017a, MNRAS, 465, 4335 Devogèle M. et al., 2017b, Submitted to Icarus statistic over the distribution of rotation periods of the Barbarian di Martino M, Blanco D., Riccioli D., de Sanctis G., 1994, Icarus, 107, 269 asteroids. We show in this work possible evidence that the Bar- Dunham, D.W., Herald, D., Frappa, E., Hayamizu, T., Talbot, J., and Timerson, barian asteroids belong to a population of rotation periods that B., Asteroid Occultations V14.0. EAR-A-3-RDR-OCCULTATIONS-V14.0. contains an excess of slow rotators, and lacks fast spinning as- NASA Planetary Data System, 2016. Durech,ˇ J., Kaasalainen, 2003, M., A&A, 709, 404 teroids. The relation between the polarimetric response and the Durech,ˇ J., Sidorin, V., Kaasalainen, M., 2010, A&A, 513, A46 unusual distribution of rotation periods is still unknown. Durechˇ J. et al.,2010, Icarus, 214, 652 Gaskell, R.W., 2008, Gaskell Eros Shape Model V1.0. NEAR-A-MSI-5- EROSSHAPE-V1.0. NASA Planetary Data System Gil-Hutton R., Cellino A., Bendjoya Ph., A&A, 2014, 569, A122 Acknowledgements Gil-Hutton R., Mesa V., Cellino A., Bendjoya P., Peñaloza L., Lovos F., 2008, The authors thank the referee for his comments, which improved A&A, 482, 309 Gil-Hutton R., 1993, Revista Mexicana de Astronomia y Astrofisica, 25, 75 the manuscript. HanušJ. et al, 2011, A&A, 530, A134 MD and JS acknowledge the support of the Université de HanušJ. et al, 2013, A&A, 551, 16 Liège. HanušJ. et al, 2017, A&A, Accepted Harris A and Young J, 1989, Icarus, 81, 314 MD and PT acknowledge the support of the French “Pro- Harris A., Young J., Dockweiler T., Gibson J., Poutanen M., Bowell E., 1992, gramme Nationale de Planétologie". Icarus, 92, 115 Part of the photometric data in this work were obtained at the Kaasalainen M., Torppa J., 2001, Icarus, 153, 24 C2PU facility (Calern Observatory, O.C.A.). Kaasalainen M., Torppa J., Muinonen K., 2001, Icarus, 153, 37 Lagerkvist, C.-I., Piironen, J., Erikson, A., 2001, Asteroid photometric cata- NP acknowledges funding from the Portuguese FCT - Foun- logue, fifth update (Uppsala Astronomical Observatory) dation for Science and Technology. CITEUC is funded by Na- Larson, S., et al., 2003, BAAS, 35, AAS/Division for Planetary Sciences Meeting tional Funds through FCT - Foundation for Science and Tech- Abstracts #35, 982 nology (project: UID/ Multi/00611/2013) and FEDER - Euro- LeCrone, C., Mills, G., Ditteon, R., 2005, MPBu, 32, 65 Mainzer et al., 2016, NEOWISE Diameters and Albedos V1.0. EAR-A- pean Regional Development Fund through COMPETE 2020 - COMPIL-5-NEOWISEDIAM-V1.0. NASA Planetary Data System. Operational Programme Competitiveness and Internationalisa- Marciniak et al, 2011, A&A, 529, A107 tion (project: POCI-01-0145-FEDER-006922). Marciniak et al, 2016, Proceedings of the Polish Astronomical Society, 3, 84

Article number, page 12 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Masiero J., Cellino A., 2009, Icarus, 199, 333 24 Departamento de Astrofísica, Universidad de La Laguna (ULL), E- Masiero J. et al., ApJ, 2011, 741, 68 38206 La Laguna, Tenerife, Spain Mothé-Diniz T., Nesvorný, D., 2008, A&A 492, 593 25 Mt. Suhora Observatory, Pedagogical University, Podchora¸˙zych2, Milani, A., Cellino A., Kneževic,´ Z., Novakovic,´ B., Spoto, F., Paolicchi, P., 30-084, Cracow, Poland 2014, Icarus, 46, 239 26 Instituto de Astrofísica de Andalucía, CSIC, Apt 3004, 18080 Nesvorný, D., Broz, M., Carruba, V., 2015, Asteroids IV Granada, Spain Oey J., 2012, MPB, 39, 145 27 Piclher F., 2009, The Minor Planet Bulletin, 36, 133 CITEUC – Centre for Earth and Space Science Research of the Uni- Schober H.J. , 1979, Astron. Astroph. Suppl., 8, 91 versity of Coimbra, Observatório Astronómico da Universidade de Sunshine et al., 2007, Lunar and Planetary Institute Science Conference Abstact, Coimbra, 3030-004 Coimbra, Portugal 1613 28 Agrupación Astronómica Región de Murcia, Orihuela, Spain Sunshine et al., 2008, Science, 320, 514 29 Arroyo Observatory, Arroyo Hurtado, Murcia, Spain Shevchenko V., Tungalag N., Chiorny V., Gaftonyuk N., Krugly Y., Harris A. 30 4438 Organ Mesa Loop, Las Cruces, New Mexico 88011 USA and Young J., 2009, Icarus, 1514 Stephens R.D., 2013, MPB, 40, 34 Stephens R.D., 2013, MPB, 40, 178 Stephens R.D., 2014, MPB, 41, 226 Appendix A: Summary of the new observations Strabla, L., Quadri, U., Girelli, R., 2013, MPBu, 40, 232 used in this work Tanga P. et al., 2015, MNRAS, 448, 3382 Tedesco, E.F, 1989, in Asteroid II, 1090 Tholen, D.J. 1984, “Asteroid Taxonomy from Cluster Analysis of Photometry”. Appendix B: Summary of previously published PhD thesis, University of Arizona. observations used in this work Usui F. et al., 2012, The Astrophysical Journal, 762, 1 Warner B.D., 2009, MPB, 36, 109 Appendix C: Light-curves obtained for this work Weidenschilling et al., 1990, Icarus, 86, 402 Appendix D: Shape models derived in this work

1 Université de Liège, Space sciences, Technologies and Astrophysics Appendix E: List of observers for the occultation Research (STAR) Institute, Allée du 6 Août 19c, Sart Tilman, 4000 data used in this work Liège, Belgium e-mail: [email protected] 2 Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange 3 Astronomical Institute, Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic 4 CdR & CdL Group: Light-curves of Minor Planets and Variable Stars, Switzerland 5 Estación Astrofísica Bosque Alegre, Observatorio Astronómico Córdoba, Argentina 6 Institute of Geology, Adam Mickiewicz University, Krygowskiego 12, 61-606 Poznan´ 7 Observatoire de Chinon, Chinon, France 8 Geneva Observatory, Switzerland 9 Astronomical Observatory Institute, Faculty of Physics, A. Mick- iewicz University, Słoneczna 36, 60-286 Poznan,´ Poland 10 Unidad de Astronomía, Fac. de Ciencias Básicas, Universidad de Antofagasta, Avda. U. de Antofagasta 02800, Antofagasta, Chile 11 Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon, Republic of Korea 12 Osservatorio Astronomico della regione autonoma Valle d’Aosta,Italy 13 School of Physics, University of Western Australia, M013, Crawley WA 6009, Australia 14 Shed of Science Observatory, 5213 Washburn Ave. S, Minneapo- lis,MN 55410, USA 15 Akdeniz University, Department of Space Sciences and Technolo- gies, Antalya, Turkey 16 TUBITAK National Observatory (TUG), 07058, Akdeniz Univer- sity Campus, Antalya, Turkey 17 Department of Physics & Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver, B.C. V6T 1Z1, Canada 18 Astrophysics Division, Institute of Physics, Jan Kochanowski Uni- versity, Swi´ etokrzyska 15,25-406 Kielce Poland 19 Laboratory of Space Researches, Uzhhorod National University, Daleka st., 2a, 88000, Uzhhorod, Ukraine 20 Institute of Physics, Faculty of Natural Sciences, University of P.J. Safarik, Park Angelinum 9, 040 01 Kosice, Slovakia 21 Stazione Astronomica di Sozzago, Italy 22 NaXys, Department of Mathematics, University of Namur, 8 Rem- part de la Vierge, 5000 Namur, Belgium 23 Instituto de Astrofísica de Canarias (IAC), E-38205 La Laguna, Tenerife, Spain

Article number, page 13 of 23 A&A proofs: manuscript no. Barbarians

Asteroid Date of observations Nlc Observers Observatory (122) Gerda 2015 Jun 09 - Jul 06 6 M. Devogèle Calern observatory, France (172) Baucis 2004 Nov 20 - 2005 Jan 29 2 F. Manzini Sozzago, Italy 2005 Feb 22 - Mar 1 3 P. Antonini Bédoin, France 2013 Mar 1 - Apr 25 10 A. Marciniak, M. Bronikowska Borowiec, Poland R. Hirsch, T. Santana, F. Berski, J. Nadolny, K. Sobkowiak 2013 Mar 4 - Apr 17 3 Ph.Bendjoya, M. Devogèle Calern observatory, France 2013 Mar 5 - Apr 16 15 P. Hickson UBC Southern Observatory, La Serena, Chile 2013 Mar 5 - 8 3 M. Todd and D. Coward Zadko Telescope, Australia 2013 Mar 29 1 F. Pilcher Organ Mesa Observatory, Las Cruces, NM 2014 Nov 13 1 M. Devogèle Calern observatory, France 2014 Nov 18 - 26 5 A. U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA (236) Honoria 2006 Apr 29 - May 3 3 R. Poncy Le Crès, France 2007 Jul 31 - Aug 2 3 J. Coloma, H. Pallares Sabadell, Barcelona, Spain 2007 Jun 21 - Aug 21 2 E. Forne, Osservatorio L’Ampolla, Tarragona, Spain 2012 Sep 19 - Dec 06 9 A. Carbognani, S. Caminiti OAVdA, Italy 2012 Aug 20 - Oct 28 6 M. Bronikowska, J. Nadolny Borowiec, Poland T. Santana, K. Sobkowiak 2013 Oct 23 - 2014 03 20 8 D. Oszkiewicz, R. Hirsch Borowiec, Poland A. Marciniak, P. Trela, I. Konstanciak, J. Horbowicz 2014 Jan 03 - Feb 19 7 F. Pilcher Organ Mesa Observatory, Las Cruces, NM 2014 Feb 07 - Feb 17 2 M. Devogèle Calern observatory, France 2014 Mar 09 - 20 2 P. Kankiewicz Kielce, Poland 2015 Mar 21 - 22 2 W. Ogłoza, A. Marciniak, Mt. Suhora, Poland V. Kudak 2015 Mar 22 - Mai 07 3 F. Pilcher Organ Mesa Observatory, Las Cruces, NM (387) Aquitania 2012 Mar 22 - May 23 4 A. Marciniak, J. Nadolny, Borowiec, Poland A. Kruszewski, T. Santana, 2013 Jun 26 - Jul 25 2 M. Devogèle Calern observatory, France 2014 Nov 19 - Dec 29 4 A. U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA K. Kaminski´ 2014 Nov 19 - Dec 18 2 M. Todd and D. Coward Zadko Telescope, Australia 2014 Dec 17 1 F. Char SARA, La Serena, Chile 2014 Dec 18 1 M. Devogèle Calern observatory, France 2015 Jan 10 - 11 2 Toni Santana-Ros, Rene Du↵ard IAA, Sierra Nevada Observatory 2015 Nov 27 - 2016 Feb 16 2 M. Devogèle Calern observatory, France (402) Chloe 2015 Jul 01 - 14 2 M.C. Quiñones EABA, Argentina (458) Hercynia 2013 May 20 - Jun 05 4 M. Devogèle Calern observatory, France 2014 Nov 27 - 28 2 M.-J. Kim, Y.-J. Choi SOAO, South Korea 2014 Nov 27 1 A. Marciniak Borowiec, Poland 2014 Nov 28 - 29 2 A.U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA 2014 Nov 29 1 M. Devogèle Calern observatory, France 2014 Nov 30 1 N. Morales La Hita, Spain (729) Watsonia 2013 Apr 04 - Jun 06 16 M. Devogèle Calern observatory, France 2014 May 26 - Jun 18 16 R. D. Stephens Santana Observatory 2015 Sep 25 1 O. Erece, M. Kaplan, TUBITAK, Turkey M.-J. Kim 2015 Oct 05 1 M.-J. Kim, Y.-J. Choi SOAO, South Korea 2015 Oct 23 - Nov 30 5 M. Devogèle Calern observatory, France (824) Anastasia 2015 Jul 05 - 25 7 M. Devogèle Calern observatory, France Table A.1. New observations used for period and shape model determination which were presented in this work and observations that are not included in the UAPC.

Article number, page 14 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

Asteroid Date of observations Nlc Observers Observatory (980) Anacostia 2005 Mar 15 - Mar 16 2 J.G. Bosch Collonges, France 2009 Feb 14 - Mar 21 6 M. Audejean Chinon, France 2012 Aug 18 - Nov 02 7 K. Sobkowiak, M. Bronikowska Borowiec M. Murawiecka, F. Berski 2013 Feb 22 - Feb 24 3 M. Devogèle Calern observatory, France 2013 Mar 27 - Apr 15 7 A. Carbognani OAVdA, Italy 2013 Dec 19 - Feb 23 11 A.U. Tomatic OAdM, Spain 2013 Dec 18 - Feb 07 2 R. Hirsch, P. Trela Borowiec, Poland 2014 Feb 22 - Mar 27 4 M. Devogèle Calern observatory, France 2014 Feb 25 - Mar 7 3 J. Horbowicz, A. Marciniak Borowiec, Poland 2014 Feb 27 1 A.U. Tomatic OAdM, Spain 2015 Mar 11 - May 28 5 F. Char SARA, La Serena, Chile 2015 Jun 09 1 M.C. Quiñones EABA, Argentina (1332) Marconia 2015 Apr 12 - May 18 8 M. Devogèle Calern observatory, France 2015 May 20 1 A.U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA 2015 Jun 03 1 R.A. Artola EABA, Argentina (1372) Haremari 2009 Nov 03 - Dec 08 8 R. Durkee Shed of Science Observatory, Minneapolis, MN, USA 2014 Dec 11 - Feb 11 7 M. Devogèle Calern observatory, France 2015 Jan 10 - 11 2 T. Santana-Ros, R. Du↵ard IAA, Sierra Nevada Observatory, Spain (1702) Kalahari 2015 Apr 29 - May 18 3 M. Devogèle Calern observatory, France 2015 May 19 1 A. U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA 2015 May 20 1 M.-J. Kim, Y.-J. Choi SOAO, South Korea 2015 Jun 04 - Jul 08 8 C.A. Alfredo EABA, Argentina (2085) Henan 2015 Jan 09 - 10 2 A. U. Tomatic OAdM, Spain 2015 Jan 11 1 T. Santana-Ros, R. Du↵ard IAA, Sierra Nevada Observatory, Spain 2015 Jan 14 - 15 2 M. Todd and D. Coward Zadko Telescope, Australia 2015 Jan 14 - Feb 11 7 M. Devogèle Calern observatory, France 2015 Mar 11 1 F. Char SARA, La Serena, Chile (3844) Lujiaxi 2014 Nov 12 - Dec 23 5 M. Devogèle Calern observatory, France 2014 Nov 20 - Dec 18 2 M. Todd and D. Coward Zadko Telescope, Australia 2014 Nov 20 1 A.U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA 2014 Dec 25 - 26 2 A.U. Tomatic OAdM, Spain (15552) 2014 Oct 29 - Nov 25 7 A. U. Tomatic, K. Kaminski´ Winer Observatory (RBT), USA Sandashounkan 2014 Oct 30 - Nov 13 2 M. Devogèle Calern obervatory, France 2014 Nov 20 1 A. U. Tomatic OAdM, Spain Table A.1. Continued

Article number, page 15 of 23 A&A proofs: manuscript no. Barbarians

Asteroid Date of observations Nlc Reference (122) Gerda 1987 Jul 28 - Aug 01 2 Shevchenko et al. (2009) 1981 Mar 13 - 25 3 di Martino et al. (1994) 1981 Mar 18 - 19 2 Gil-Hutton (1993) 2003 Mai 02 - 09 3 Shevchenko et al. (2009) 2005 Sep 11 - Oct 04 2 Shevchenko et al. (2009) 2005 Sep 31 - Nov 28 3 Buchheim et al. (2007) 2009 Apr 01 - 03 3 Pilcher (2009) (172) Baucis 1984 May 11 1 Weidenschilling et al. (1990) 1989 Nov 21 1 Weidenschilling et al. (1990) (236) Honoria 1979 Jul 30 - Aug 22 7 Harris and Young (1989) 1980 Dec 30 - 1981 Feb 1 7 Harris and Young (1989) (387) Aquitania 1979 Aug 27 - 29 3 Schober et al. (1979) 1981 May 30 1 Barucci et al. (1985) 1981 May 30 - Jul 24 8 Harris et al. (1992) (402) Chloe 1997 Jan 19 - Mar 02 5 Denchev et al. (2000) 2009 Feb 07 - 17 4 Warner (2009) 2014 May 15 - 16 2 Stephens (2014) (458) Hercynia 1987 Feb 18 1 Binzel (1987) (729) Watsonia 2013 Jan 21 - Feb 14 8 Stephens (2013) (980) Anacostia 1980 Jul 20 - Aug 18 5 Harris and young (1989) (1332) Marconia 2012 Aug 27 - Sep 11 6 Stephens (2013) (1702) Kalahari 2011 Jul 28 - Aug 26 10 Oey (2012) Table B.1. All observations used for period and shape modelling which have already been published.

Article number, page 16 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

3.1 7.3 C2PU 150609 Sozzago 041120 3.12 C2PU 150624 7.35 Sozzago 050129 C2PU 150625 Bédoin 050222 C2PU 150630 Bédoin 050223 3.14 C2PU 150705-06 7.4 Bédoin 050301

3.16 7.45

3.18 7.5

3.2 7.55

3.22 7.6 Relative magnitude Relative magnitude 3.24 7.65

3.26 7.7

3.28 7.75 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (122) Gerda: 2015 opposition; P = 10.6872 0.0001 h (172) Baucis: 2004-2005 opposition; P = 27.417 0.005 h syn ± syn ± 11.8 1.34 Borowiec 130103 C2PU 141113 Borowiec 130303 1.36 RBT 141118 Borowiec 130403 RBT 141119 11.85 Borowiec 130503 RBT 141121 Hickson 130503 1.38 RBT 141125 Hickson 130903 RBT 141126 Hickson 131003 Hickson 131203 1.4 11.9 Borowiec 130313 Hickson 131403 1.42 Borowiec 131403 Hickson 131803 Hickson 131903 1.44 11.95 Hickson 132103 Hickson 132203 1.46

Relative magnitude Borowiek 132903 Relative magnitude Hickson 131504 1.48 12

1.5

12.05 1.52 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (172) Baucis: 2013 opposition; P = 27.4096 0.0004 h (172) Baucis: 2014 opposition; P = 27.42 0.01 h syn ± syn ± 12.92 11.16 Cres 060429 Ampolla 070621 Cres 060430 11.18 Sabadell 070731 12.93 Cres 060503 Sabadell 070802 Ampolla 070821 11.2 12.94 11.22

12.95 11.24

12.96 11.26

11.28 Relative magnitude 12.97 Relative magnitude 11.3 12.98 11.32

12.99 11.34 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (236) Honoria: 2006 opposition; P = 12.35 0.10 h (236) Honoria: 2007 opposition; P = 12.34 0.02 h syn ± syn ± -3.15 0.25 Borowiec 120819 Borowiec 150321 Borowiec 120823 Borowiec 150322 Borowiec 120829 Organ Mesa 150322 -3.1 OAVdA 120919 Organ Mesa 150326 OAVdA 120920 Organ Mesa 150507 OAVdA 120921 Borowiec 120923 OAVdA 121003 0.3 -3.05 OAVdA 121010 OAVdA 121012 Borowiec 121018 Borowiec 121028 OAVdA 121116 -3 OAVdA 121206 0.35 Relative magnitude Relative magnitude

-2.95

-2.9 0.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (236) Honoria: 2012 opposition; P = 12.337 0.001 h (236) Honoria: 2015 opposition; P = 12.33 0.01 h syn ± syn ± Fig. C.1. Composite light-curves of asteroids studied in this works.

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0.85 -0.34 Borowiec 120322 C2PU 130626 Borowiec 120423 C2PU 130725 Borowiec 120425 -0.33 Borowiec 120523 0.9 -0.32

-0.31

0.95 -0.3

-0.29 Relative magnitude Relative magnitude 1 -0.28

-0.27

1.05 -0.26 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (387) Aquitania: 2012 opposition; P = 24.15 0.02 h (387) Aquitania: 2013 opposition; P = 24.15 0.15 h syn ± syn ± 1.1 3.54 ZADKO 141101 C2PU 151127 RBT 141119 C2PU 160225 SARA 141217 3.56 1.15 C2PU 141218 RBT 141227 RBT 141228 3.58 RBT 141229 IAA 150110 1.2 IAA 150111 3.6

3.62 1.25

Relative magnitude Relative magnitude 3.64 1.3 3.66

1.35 3.68 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (387) Aquitania: 2014-2015 opposition; P = 24.14 0.02 h (387) Aquitania: 2015-2016 opposition; P = 24.147 h syn ± syn -0.1 3.94 EABA 150701 C2PU 130520 EABA 150714 C2PU 130521 C2PU 130604 3.96 -0.05 C2PU 130605

3.98 0

4

0.05 4.02 Relative magnitude Relative magnitude

0.1 4.04

0.15 4.06 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (402) Chloe: 2015 opposition; P = 10.70 0.05 h (458) Hercynia: 2013 opposition; P = 21.8 0.1h syn ± syn ± -0.2 1.8 SOAO 141027 TUBITAK 150925 Borowiec 141027 SOAO 151005 -0.1 RBT 141028 C2PU 151023 SOAO 141028 1.85 C2PU 151101 C2PU 141029 C2PU 151125 0 RBT 141029 C2PU 151127 La Hita 141030 C2PU 151130 RBT 141030 1.9 0.1

0.2 1.95

Relative magnitude 0.3 Relative magnitude 2 0.4

0.5 2.05 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 Rotational phase Rotational phase (458) Hercynia: 2014 opposition; P = 21.81 0.03 h (729) Watsonia: 2015 opposition; P = 25.190 0.003 h syn ± syn ± Fig. C.1. Continued

Article number, page 18 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

2 13.35 C2PU 150705 Collonges 050315 2.1 C2PU 150706 Collonges 050316 C2PU 150708 2.2 C2PU 150709 13.4 C2PU 150710 C2PU 150725 2.3

2.4 13.45

2.5

2.6 13.5 Relative magnitude 2.7 Relative magnitude

2.8 13.55

2.9

3 13.6 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (824) Anastasia: 2015 opposition; P = 252 h (980) Anacostia: 2005 opposition; P = 20.1 0.1h syn syn ± 12.55 -1.33 Chinon 090214 Borowiec 150818 Chinon 090225 Borowiec 150823 Chinon 090315 -1.32 Borowiec 150827 12.6 Chinon 090316 Borowiec 150913 Chinon 090317 Borowiec 150921 Chinon 090321 -1.31 Borowiec 150930 Borowiec 151102 12.65

-1.3 12.7 -1.29

12.75 Relative magnitude Relative magnitude -1.28

12.8 -1.27

12.85 -1.26 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (980) Anacostia: 2009 opposition; P = 20.124 0.001 h (980) Anacostia: 2012 opposition; P = 20.17 0.01 h syn ± syn ± 1.38 2 OAdM 131205 SARA 150311 1.4 OAdM 131209 2.01 SARA 150331 OAdM 131211 SARA 150409 1.42 OAdM 131215 2.02 SARA 150429 Borowiec 131217 EABA 150611 Borowiec 140206 1.44 OAdM 140221 2.03 C2PU 140223 1.46 Borowiec 140224 2.04 C2PU 140224 1.48 C2PU 140225 2.05 Borowiec 140301 Borowiec 140307 1.5 C2PU 140327 2.06 OAVdA 140331

Relative magnitude 1.52 OAVdA 140405 Relative magnitude 2.07 OAVdA 140406 1.54 OAVdA 140408 2.08 OAVdA 140410 OAVdA 140415 1.56 2.09

1.58 2.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (980) Anacostia: 2013-2014 opposition; P = 20.1137 0.0002 h (980) Anacostia: 2015 opposition; P = 20.16 0.01 h syn ± syn ± 2.6 0.92 C2PU 150412 Shed 091103 2.65 C2PU 150415 Shed 091105 C2PU 150420 0.94 Shed 091108 C2PU 150423 Shed 091110 2.7 C2PU 150428 Shed 091115 C2PU 150429 0.96 Shed 091117 C2PU 150430 Shed 091211 2.75 C2PU 150518 Shed 091215 RBT 150520 0.98 2.8 EABA 150603 1 2.85 1.02 2.9 Relative magnitude Relative magnitude 1.04 2.95

3 1.06

3.05 1.08 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (1332) Marconia, P = 32.1201 0.0005 h (1372) Haremari: 2009 opposition; P = 15.22 0.01 h syn ± syn ± Fig. C.2. Continued

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2.24 -1.3 C2PU 141211 C2PU 150429 2.245 C2PU 141221 C2PU 150430 IAA 150111 -1.25 C2PU 150518 C2PU 150117 RBT 150519 2.25 C2PU 150201 SOAO 150520 C2PU 150209 -1.2 EABA 150604 C2PU 150210 EABA 150615 2.255 C2PU 150211 EABA 150623 -1.15 EABA 150707 2.26 EABA 150708 -1.1 2.265 -1.05 2.27 Relative magnitude Relative magnitude -1 2.275

2.28 -0.95

2.285 -0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Rotational phase Rotational phase (1372) Haremari, P = 15.24 0.03 h (1702) Kalahari, P = 21.15 0.03 h syn ± syn ± 1.35 3.7 OAdM 150109 C2PU 141112 1.4 OAdM 150110 C2PU 141113 IAA 150111 3.75 RBT 141120 1.45 C2PU 150114 C2PU 141211 ZADKO 150114-15 ZADKO 141218 C2PU 150117 3.8 C2PU 141221 1.5 C2PU 150131 C2PU 141223 C2PU 150201 OAdM 141225 3.85 1.55 C2PU 150209 OAdM 141226 C2PU 150210 1.6 C2PU 150211 3.9 SARA 150311 1.65 3.95

Relative magnitude 1.7 Relative magnitude 4 1.75 4.05 1.8

1.85 4.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (2085) Henan, P = 110.5 1 h (94.3 1 h) (3844) Lujiaxi, P = 13.33 0.01 h syn ± ± syn ± -1 -0.25 RBT 141029 C2PU 141025 C2PU 141030 C2PU 141031 -0.8 C2PU 141113 -0.2 C2PU 150114 RBT 141117 RBT 141118 -0.15 -0.6 RBT 141119 ZADKO 141119-20 RBT 141120 OAdM 141120 -0.1 -0.4 RBT6 141124 RBT7 141125 -0.05 -0.2 0

Relative magnitude 0 Relative magnitude 0.05

0.2 0.1

0.4 0.15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Rotational phase Rotational phase (15552) Sandashounkan, P = 33.62 0.3h (67255) 2000ET109, P = 3.70 0.01 h syn ± syn ± Fig. C.2. Continued

Article number, page 20 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

(172) Baucis, pole solution (209, 22).

(387) Aquitania, pole solution (142, 51).

(402) Chloe, pole solution (306, 61). Fig. D.1. Asteroid shape models derived in this work. For each shape model, the reference system in which the shape is described by the inversion procedure, is also displayed. The z axis corresponds to the rotation axis. The y axis is oriented to correspond to the longest direction of the shape model on the plane perpendicular to z. Each shape is projected along three di↵erent viewing geometries to provide an overall view. The first one (left-most part of the figures) corresponds to a viewing geometry of 0 and 0 for the longitude and latitude respectively (the x axis is facing the observer). The second orientation corresponds to (120, 30) and the third one to (240, 30). The inset plot shows the result of the Bootstrap method. The x axis corresponds to the number of light-curves used and the y axis is ⌘a. Since the shape model of (387) Aquitania was derived without sparse data, the bootstrap method was not applied.

Article number, page 21 of 23 A&A proofs: manuscript no. Barbarians

(458) Hercynia, pole solution (274, 33).

(729) Watsonia, pole solution (88, 79)

(980) Anacostia, pole solution (23, 30) Fig. D.1. Continued

Article number, page 22 of 23 Devogèle et al.: Shape and spin determination of Barbarian asteroids

List of observers (172) Baucis (2015-12-18) J.A. de los Reyes, Sensi Pastor, SP F. Reyes, SP J.L. Ortiz, SP F. Aceituno, SP

(236) Honoria (2008-10-11) S Conard, Gamber, MD, USA R Cadmus, Grinnell, IA, USA

(236) Honoria (2012-09-07) C. Schnabel, SP C. Perello, A. Selva, SP U. Quadri, IT P. Baru↵etti, IT J. Rovira, SP

(387) Aquitania (2013-07-26) T. Blank, West of Uvalde, TX, USA T. Blank, Uvalde, TX , USA T. Blank, D’Hanis, TX, USA T. Blank, Devine, TX, USA S. Degenhardt, Moore, TX, USA M. McCants, TX, USA S. Degenhardt, Bigfoot, TX, USA S. Degenhardt, Poteet, TX, USA S. Degenhardt, Pleasanton, TX, USA

(402) Chloe (2004-12-15) R. Nugent, Bu↵alo, TX, USA R. Venable, Bunnell, FL, USA R. Venable, DeLand, FL, USA J. Stamm, Oro Valley, AZ, USA R. Peterson, Scottsdale, AZ, USA B. Cudnik, Houston, TX, USA

(402) Chloe (2004-12-23) S. Preston, Ocean Park, WA, USA J. Preston, Ilwaco, WA, USA T. George, Moro, OR, USA Fig. E.1. List of observers of stellar occultation by an asteroid.

Article number, page 23 of 23